Monte Carlo method for the real and complex fuzzy system of linear algebraic equations

2019 ◽  
Vol 24 (2) ◽  
pp. 1255-1270
Author(s):  
Behrouz Fathi-Vajargah ◽  
Zeinab Hassanzadeh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fuzzy System ◽  
Algebraic Equations ◽  
The Real ◽  
Linear Algebraic Equations

scholarly journals Monte Carlo method for solving a parabolic problem

2016 ◽  
Vol 20 (3) ◽  
pp. 933-937
Author(s):  
Yi Tian ◽  
Zai-Zai Yan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Random Sampling ◽  
Parabolic Problem ◽  
Test Problems ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Sparse System ◽  
Linear Algebraic Equations ◽  
Crank Nicolson

In this paper, we present a numerical method based on random sampling for a parabolic problem. This method combines use of the Crank-Nicolson method and Monte Carlo method. In the numerical algorithm, we first discretize governing equations by Crank-Nicolson method, and obtain a large sparse system of linear algebraic equations, then use Monte Carlo method to solve the linear algebraic equations. To illustrate the usefulness of this technique, we apply it to some test problems.

scholarly journals A new method for solving a class of heat conduction equations

2015 ◽  
Vol 19 (4) ◽  
pp. 1205-1210
Author(s):  
Yi Tian ◽  
Zai-Zai Yan ◽  
Zhi-Min Hong
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Dimensional Space ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Governing Equations ◽  
One Dimensional ◽  
Sparse System ◽  
Linear Algebraic Equations ◽  
Crank Nicolson

A numerical method for solving a class of heat conduction equations with variable coefficients in one dimensional space is demonstrated. This method combines the Crank-Nicolson and Monte Carlo methods. Using Crank-Nicolson method, the governing equations are discretized into a large sparse system of linear algebraic equations, which are solved by Monte Carlo method. To illustrate the usefulness of this technique, we apply it to two problems. Numerical results show the performance of the present work.

Influence Functions in the Numerical Analysis of Bending of Thin Elastic Plates

1984 ◽  
Vol 8 (2) ◽  
pp. 103-114 ◽  
Author(s):  
Mohammed F.N. Mohsen ◽  
Ali A. Al-Gadhib ◽  
Mohammed H. Baluch
Keyword(s):  
Boundary Conditions ◽  
Influence Function ◽  
Infinite Plate ◽  
Thin Plates ◽  
Influence Functions ◽  
Algebraic Equations ◽  
Elastic Plates ◽  
The Real ◽  
Linear Algebraic Equations ◽  
The Moment

A numerical method for the linear analysis of thin plates of arbitrary plan form and subjected to arbitrary loading and boundary conditions is presented in this paper. This method is an extension of the Wu-Altiero method [1] where use has been made of the force influence function for an infinite plate, whereas the work contained in this paper is based on the use of the moment influence function of an infinite plate. The technique basically involves embedding the real plate into a fictitious infinite plate for which the moment influence function is known. N points are prescribed at the plate boundary at which the boundary conditions for the original problem are collocated by means of 2N fictitious moments placed around contours outside the domain of the real plate. A system of 2N linear algebraic equations in the unknown moments is obtained. The solution of the system yields the unknown moments. These may in turn be used to compute deflection, moments or shear at any point in the thin plate. Finally, the method is extended to include influence functions of both concentrated forces and concentrated moments. This is obtained by applying concentrated moments and forces simultaneously on the contours located outside the domain of the plate.

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